Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient
| Autor: | Manuel E. Lladser, Stephen R. Chestnut |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Doeblin
occupancy distribution General Computer Science Markov chain Approximations of π motif Ergodicity Markov process compound Poisson approximation [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS] Type inequality Markov chain embedding technique pattern Theoretical Computer Science [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO] symbols.namesake [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM] [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG] Homogeneous Elementary proof symbols Discrete Mathematics and Combinatorics Embedding Statistical physics Mathematics |
| Popis: | We state and prove new properties about Doeblin's ergodicity coefficient for finite Markov chains. We show that this coefficient satisfies a sub-multiplicative type inequality (analogous to the Markov-Dobrushin's ergodicity coefficient), and provide a novel but elementary proof of Doeblin's characterization of weak-ergodicity for non-homogeneous chains. Using Doeblin's coefficient, we illustrate how to approximate a homogeneous but possibly non-stationary Markov chain of duration $n$ by independent and short-lived realizations of an auxiliary chain of duration of order $\ln (n)$. This leads to approximations of occupancy distributions in homogeneous chains, which may be particularly useful when exact calculations via one-step methods or transfer matrices are impractical, and when asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|